Introduction to Analysis (Dover Books on Mathematics)

By Maxwell Rosenlicht

This well-written textual content presents first-class guideline in simple genuine research, giving a superior origin for direct access into complex paintings in such fields as advanced research, differential equations, integration thought, and normal topology. The nominal prerequisite is a yr of calculus, yet truly not anything is thought except the axioms of the genuine quantity method. as a result of its readability, simplicity of exposition, and pressure on more uncomplicated examples, this fabric is available to quite a lot of scholars, of either arithmetic and different fields.
Chapter headings contain notions from set idea, the genuine quantity procedure, metric areas, non-stop features, differentiation, Riemann integration, interchange of restrict operations, the strategy of successive approximations, partial differentiation, and a number of integrals.
Following a few introductory fabric on very uncomplicated set concept and the deduction of an important homes of the true quantity method from its axioms, Professor Rosenlicht will get to the guts of the e-book: a rigorous and thoroughly awarded dialogue of metric areas and non-stop features, together with such subject matters as open and closed units, limits and continuity, and convergent series of issues and of services. next chapters hide easily and successfully the proper features of trouble-free calculus including numerous a bit of extra complex topics, resembling multivariable calculus and lifestyles theorems. The workouts comprise either effortless difficulties and tougher ones, fascinating examples and counter examples, and a few extra complicated results.
Introduction to Analysis lends itself to a one- or two-quarter or one-semester path on the undergraduate point. It grew out of a direction given at Berkeley considering 1960. Refinement via vast school room use and the author’s pedagogical event and services make it an surprisingly available introductory text.

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Partial Differential Equations: Theory and Completely Solved Problems

By Thomas Hillen

Uniquely presents absolutely solved difficulties for linear partial differential equations and boundary price problems

Partial Differential Equations: conception and fully Solved Problems makes use of real-world actual versions along crucial theoretical innovations. With wide examples, the booklet courses readers by utilizing Partial Differential Equations (PDEs) for effectively fixing and modeling phenomena in engineering, biology, and the utilized sciences.

The e-book focuses solely on linear PDEs and the way they are often solved utilizing the separation of variables procedure. The authors commence via describing capabilities and their partial derivatives whereas additionally defining the ideas of elliptic, parabolic, and hyperbolic PDEs. Following an creation to easy concept, next chapters discover key subject matters including:

• category of second-order linear PDEs

• Derivation of warmth, wave, and Laplace’s equations

• Fourier series

• Separation of variables

• Sturm-Liouville theory

• Fourier transforms

Each bankruptcy concludes with summaries that define key suggestions. Readers are supplied the chance to check their comprehension of the awarded fabric via quite a few difficulties, ranked by means of their point of complexity, and a similar web site beneficial properties supplemental info and resources.

Extensively class-tested to make sure an obtainable presentation, Partial Differential Equations is a wonderful booklet for engineering, arithmetic, and utilized technology classes at the subject on the upper-undergraduate and graduate levels.

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Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and Its Applications Series, Book 75)

By Irena Lasiecka, Roberto Triggiani

This can be the 1st quantity of a accomplished and up to date therapy of quadratic optimum regulate thought for partial differential equations over a finite or countless time horizon, and comparable differential (integral) and algebraic Riccati equations. The authors describe either non-stop thought and numerical approximation. They use an summary house, operator theoretic technique, in accordance with semigroups tools and unifying throughout a number of uncomplicated sessions of evolution. some of the summary frameworks are encouraged by way of, and eventually directed to, partial differential equations with boundary/point keep watch over.

Volume I comprises the summary parabolic idea (continuous thought and numerical approximation conception) for the finite and endless circumstances and corresponding PDE illustrations, and provides quite a few new effects. those volumes will entice graduate scholars and researchers in natural and utilized arithmetic and theoretical engineering with an curiosity in optimum keep watch over difficulties.

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Geometric Problems on Maxima and Minima

By Titu Andreescu

Presents enormous quantities of utmost price difficulties, examples, and strategies basically via Euclidean geometry

Unified method of the topic, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning

Applications to physics, engineering, and economics

Ideal to be used on the junior and senior undergraduate point, with wide appeal to students, teachers, professional mathematicians, and puzzle enthusiasts

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Vector Analysis Versus Vector Calculus (Universitext)

By Antonio Galbis, Manuel Maestre

The goal of this ebook is to facilitate using Stokes' Theorem in applications.  The textual content takes a differential geometric viewpoint and gives for the coed a bridge among natural and utilized arithmetic by way of rigorously development a proper rigorous improvement of the subject and following this via to concrete purposes in and 3 variables.

Key themes contain vectors and vector fields, line integrals, average k-surfaces, flux of a vector box, orientation of a floor, differential types, Stokes' theorem, and divergence theorem.
 
This ebook is meant for top undergraduate scholars who've accomplished a regular advent to differential and essential calculus for services of a number of variables.  The e-book is additionally beneficial to engineering and physics scholars who know the way to deal with the theorems of eco-friendly, Stokes and Gauss, yet wish to discover the subject further.

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Riemannian Geometry (Graduate Texts in Mathematics, Vol. 171)

By Peter Petersen

This quantity introduces strategies and theorems of Riemannian geometry, and opens how you can complicated themes. The textual content combines the geometric elements of Riemannian geometry with analytic features of the speculation, and reports fresh study. The up-to-date moment version encompasses a new coordinate-free formulation that's simply remembered (the Koszul formulation in disguise); an accelerated variety of coordinate calculations of connection and curvature; basic fomulas for curvature on Lie teams and submersions; variational calculus built-in into the textual content, taking into consideration an early remedy of the field theorem utilizing a forgotten facts via Berger; contemporary effects concerning manifolds with optimistic curvature.

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100 Great Problems of Elementary Mathematics (Dover Books on Mathematics)

"The assortment, drawn from mathematics, algebra, natural and algebraic geometry and astronomy, is awfully attention-grabbing and attractive." — Mathematical Gazette
This uncommonly fascinating quantity covers a hundred of the main well-known ancient difficulties of common arithmetic. not just does the booklet undergo witness to the intense ingenuity of a few of the best mathematical minds of heritage — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and so on — however it presents infrequent perception and thought to any reader, from highschool math pupil to expert mathematician. this is often certainly an strange and uniquely useful book.
The 100 difficulties are awarded in six different types: 26 arithmetical difficulties, 15 planimetric difficulties, 25 vintage difficulties referring to conic sections and cycloids, 10 stereometric difficulties, 12 nautical and astronomical difficulties, and 12 maxima and minima difficulties. as well as defining the issues and giving complete recommendations and proofs, the writer recounts their origins and background and discusses personalities linked to them. usually he supplies now not the unique resolution, yet one or less complicated or extra fascinating demonstrations. in just or 3 circumstances does the answer suppose whatever greater than an information of theorems of straight forward arithmetic; for this reason, it is a booklet with a very large appeal.
Some of the main celebrated and fascinating goods are: Archimedes' "Problema Bovinum," Euler's challenge of polygon department, Omar Khayyam's binomial enlargement, the Euler quantity, Newton's exponential sequence, the sine and cosine sequence, Mercator's logarithmic sequence, the Fermat-Euler leading quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' decision of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 common solids, the Mercator projection, the Kepler equation, selection of the placement of a boat at sea, Lambert's comet challenge, and Steiner's ellipse, circle, and sphere problems.
This translation, ready in particular for Dover through David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language viewers for the 1st time.

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A Course on Finite Groups (Universitext)

By H.E. Rose

Introduces the richness of workforce thought to complex undergraduate and graduate scholars, focusing on the finite aspects.

Provides a wealth of routines and difficulties to help self-study.

Additional on-line assets on tougher and extra specialized themes can be utilized as extension fabric for classes, or for extra self reliant study.

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What's Luck Got to Do with It?: The History, Mathematics, and Psychology of the Gambler's Illusion

By Joseph Mazur

Why accomplish that many gamblers possibility all of it after they comprehend the chances of profitable are opposed to them? Why do they think cube are "hot" in a successful streak? Why can we count on heads on a coin toss after numerous flips have grew to become up tails? What's success obtained to Do with It? takes a full of life and eye-opening examine the math, heritage, and psychology of playing to bare the main broadly held misconceptions approximately good fortune. It exposes the risks of feeling fortunate, and makes use of the maths of predictable results to teach while our probabilities of profitable are literally good.

Mathematician Joseph Mazur lines the heritage of playing from the earliest identified archaeological facts of cube enjoying between Neolithic peoples to the 1st systematic mathematical reports of video games of probability through the Renaissance, from government-administered lotteries to the glittering seductions of grand casinos, and directly to the worldwide monetary main issue as a result of financiers' trillion-dollar bets. utilizing lots of enticing anecdotes, Mazur explains the maths at the back of gambling--including the legislation of chance, facts, having a bet opposed to expectancies, and the legislation of huge numbers--and describes the mental and emotional components that appeal to humans to place their religion in profitable that ever-elusive jackpot regardless of its mathematical improbability.

As unique because it is informative, What's good fortune received to Do with It? demonstrates the pervasive nature of our trust in success and the misleading psychology of successful and losing.

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